The Stacks project

Remark 47.13.5. Let $A$ be a ring and let $I \subset A$ be an ideal. Set $B = A/I$. In this case the functor $\mathop{\mathrm{Hom}}\nolimits _ A(B, -)$ is equal to the functor

which sends $M$ to the submodule of $I$-torsion.